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# Completing the Square Day 1 of 2

Lesson 7 of 12

## Objective: Students will be able to complete the square to solve a quadratic equation with both real and complex roots.

## Big Idea: Compare and contrast the effectiveness of multiple methods of solving quadratic equations.

*50 minutes*

#### Warm up and Homework Review

*10 min*

I include **Warm ups** with a **Rubric** as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The resource video specifically explains this lesson’s Warm Up- Complete the Square, which asks students to determine two methods to solve x^{2 }= 9.

I also use this time to correct and record the previous day's Homework.

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#### Complete the Square

*37 min*

Please watch my Video Narrative on teaching completing the square.

We are going to begin by looking at an area problem similar to the problems seen in the last unit on solving polynomials by factoring (**Math Practice 4**). This gives us a frame for the problems we will be able to solve using the new techniques learned in this unit.

After doing several quadratics that can be solved by taking the square root of each side, we then look at the perfect square trinomial identity in preparation for learning to complete the square (**Math Practice 8**). This pattern is the key to students successfully understanding how complete the square works.

Once they have this pattern mastered, we do a completing the square Guided Practice. We look at these problems graphically once we have solved them to compare the methods of solutions (**Math Practice 5**). This will be particularly meaningful as we look at irrational and complex solutions and the inaccuracy of their graphical solutions (**Math Practice 6**).

Please see the PowerPoint for detailed presentation notes.

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#### Exit Ticket

*3 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket asks students to solve a quadratic equation by completing the square.

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This equation is meant to reinforce the lesson and ensure that the students can independently solve a quadratic equation by completing the square. It also includes an application problem similar to those introduce, but not solved, at the beginning of the lesson.** **

This worksheet was created with Kuta Software which is an amazing resource for any mathematics teacher.

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: The Real Number System
- LESSON 2: Simplifying Square Roots
- LESSON 3: Imaginary Numbers Day 1 of 2
- LESSON 4: Imaginary Numbers Day 2 of 2
- LESSON 5: Complex Numbers Day 1 of 2
- LESSON 6: Complex Numbers Day 2 of 2
- LESSON 7: Completing the Square Day 1 of 2
- LESSON 8: Completing the Square Day 2 of 2
- LESSON 9: Real and Complex Number System Quiz
- LESSON 10: Quadratic Formula
- LESSON 11: Complex Numbers and Quadratic Equations Review
- LESSON 12: Complex Numbers and Quadratic Equations Test